Al-Khwarizmi
Applied Mathematics Webinar 

Next talk : May 12, 2026. 

Tuesday - 2:00 pm (GMT) 

Zoom link: https://ksu-hub.zoom.us/j/97753107489

Speaker:  Mokhtar Alaya, University of de Technology of  Compiègne, France.  

Title: Optimal Transport Meets Privacy: Gaussian-Smoothed Divergences for Private Distribution Learning and Domain Adaptation.  

Abstract: Optimal Transport (OT) offers a principled framework for domain adaptation by aligning source and target data distributions through cost-minimizing mass transport. In this talk, we introduce OT from the Monge formulation and show how transport plans yield interpretable couplings between samples while preserving underlying geometry. We then focus on Gaussian-smoothed sliced divergences, a way to compare probability distributions that introduces privacy protection through Gaussian noise. This smoothing does not break the desirable properties of the underlying distances: the resulting quantities still behave like proper metrics, remain well behaved statistically, and stay practical in high dimensions. We also explain a key theoretical contribution, namely a double-sampling viewpoint that allows us to analyze convergence rates and approximation error in a clean way. Finally, we present experiments on domain adaptation benchmarks demonstrating that we can obtain privacy with little loss in performance, while making it easier to explore the privacy–utility trade-off in practice.

This a joint work with A. Rakotomamonjy (Criteo Paris), M. Bérard (Univ. Rouen) and G. Gasso (INSA Rouen).

Paper : Gaussian-Smoothed Sliced Probability Divergences, published in Transactions on Machine Learning Research, 2024